Question

Suppose xy = 15, where x and y are functions of t. What is the value of dx/dt when x = 3 and dy/dt = −2?

a. 15
b. 2.5
c. −1.2
d. 5

Answer 1

The value of dx/dt given x = 3 and dy/dt = -2, with xy = 15, is -0.4 by using the product rule for differentiation.

Step-by-step explanation:

To find the value of dx/dt when x = 3 and dy/dt = -2, given that xy = 15, we can use the product rule for differentiation which tells us how to differentiate functions that are products of two other functions. According to the product rule d(uv)/dt = u(dv/dt) + v(du/dt), where u and v are functions of t. In this case, u = x(t) and v = y(t).

Substituting the values into the product rule, we get:

The negative sign indicates that as t increases, x is decreasing at the moment in question. To complete this calculation, we put the dx/dt over a common denominator of 15 which simplifies down to -2/5 or -0.4 after reducing.